Was I the only one thinking of Theon's messy execution when Ygritte said to Jon to strike her head off clean or she'll haunt him?
As a slight aside, many many centuries ago when faced with the executioner, it was common practice to tip the guy with the axe to ensure a good job. If you didn't tip, or just didn't tip well enough, he could make sure the chop wasn't clean.
At the Tower of London, James Scott the Duke of Monmouth refused to tip the executioner. Big mistake. After 8 swings of his axe, Scott stopped whimpering and fell silent but his head was still attached. The job was finished because a knife was produced to make the final cut.
Again at the Tower, The Countess of Salisbury was struck 11 times before her head finally came off. This was really because the executioner was a n00b and his first strike missed her neck altogether, instead going deep into her shoulders. He had to chase her down in front of a gasping crowd. They got the price of admission that day.
If you were to ever doubt the things you see in GoT as being overly dramatic or unnecessarily cruel, forget it. The Middle Ages were far, far worse.